NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 1 Nonlinear force-free extrapolation of coronal magnetic fields T. Wiegelmann, J.K. Thalmann, B. Inhester Coronal magnetic field models Nonlinear Force-Free Fields (NLFFF) Consistency criteria for vector magnetograms and preprocessing Evolution of a flaring Active Region Non-force-free fields Conclusions

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 2 Force-free magnetic field j x B ~ 0 Vector magnetogram measurements from Gary, Sol. Phys NOT Force-free

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 3 NonLinear Force-Free Fields Compute initial a potential field (Requires only B n on bottom boundary) Iterate for NLFFF-field, Boundary conditions: - B n and J n for positive or negative polarity on boundary (Grad-Rubin method) - Magnetic field vector B x B y B z on boundary (MHD-relaxation, Optimization method) Equivalent

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 4 Grad-Rubin method Amari et al. 1997,2006, Wheatland 2004,06,07

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 5 MHD-relaxation Chodura & Schlueter 1981, Valori et al Optimization Wheatland et al. 2000, Wiegelmann 2004 NLFFF-consortium (Schrijver et al. 2006): Optimization most accurate and fastest method.

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 6 Consistency criteria for vectormagnetograms (Aly 1989) If these relations are NOT fulfilled on the boundary, then the photospheric data are inconsistent with the force-free assumption. NO Force-Free-Field.

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 7 No net forceNo net torquePhotosphereSmoothnessPreprocessed boundary data

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 8 Preprocessing of vector magnetograms (Wiegelmann, Inhester, Sakurai, Sol. Phys. 2006) Use photospheric field vector as input. Preprocessing provides consistent boundary data for nonlinear force-free modeling. Boundary is not in the photosphere (which is NOT force-free). The preprocessed boundary data are chromospheric like. Preprocessing can be improved by including chromospheric observations. (Wiegelmann, Thalmann, Schrijver, DeRosa, Metcalf, Sol. Phys. 2008)

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 9 Chromospheric H-alpha preprocessing H-alpha fibrils outline magnetic field lines. With image-recognition techniques we get tangent to the chromospheric magnetic field vector (Hx, Hy). Idea: include a term in the preprocessing to minimize angle of preprocessed magnetic field (Bx,By) with (Hx,Hy).

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 10 Test: Model Active Region ( van Ballegooijen et al. 2007, Aad’s model) Model contains the (not force-free) photospheric magnetic field vector and an almost force-free chromosphere and corona.

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 11 Comparison of NLFFF-codes with Aad’s model Metcalf et al., Sol. Phys Good agreement for extrapolations from chromosphere. -Poor results for using photospheric data directly. -Improvement with preprocessed photospheric data.

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 12 Prepro- cessing We test preprocessing with Aad’s model

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 13 Angle in Chromosphere Force-free coronal magnetic Energy No pre- processing 19 o 65% Classical pre- processing 9 o 97% H-Alpha pre- processing 1 o 100% Results: Comparison with Aad‘s Model

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 14 Evolution of flaring Active Region NOAA (Extrapolation (optimization) from NAOJ/SFT-vector magnetograms; Thalmann & Wiegelmann, A&A 2008, in press) Solar Flare Telescope, Mitaka, Tokyo, (Sakurai et al. 1995, operating since 1992)

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 15 Flaring Active Region NOAA 10540

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 16 Magnetic energy builds up and is releases during flare Plan: Study flaring ARs with higher time cadence with SDO

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 17 Next step: Magnetohydrostatics Lorentz force pressure gradient gravity Magnetohydrostatic optimization code Cartesian: (Wiegelmann, Neukirch, A&A 2006) Spherical: (Wiegelmann, Neukirch, Ruan, Inhester, A&A 2007) Codes work correctly for smooth test cases To Do: Application to Data (STEREO,SDO)

NJIT-seminar Newark, NJITWiegelmann et al: Nonlinear force-free fields 18